In general, signal processing refers to the techniques and processes by which analog and digital signals are created, transmitted, received, and interpreted, among other functions. In many instances, the signals are electromagnetic signals that are processed using various electrical circuits, one common type of which is filter circuits (“filters”), which operate in a frequency-dependent manner to completely or partially suppress or remove one or more components of a given signal. Thus, a given filter may receive a signal having a number of different components in the frequency domain, and operate to output only a subset of those components while suppressing the others, which could represent interference or noise, among other possibilities.
As is known in the art, filters come in many shapes and sizes. A common delineation among filters is between passive filters and active filters. Passive filters include only reactive (i.e., non-powered) circuit elements such as resistors, capacitors, and inductors. Active filters include at least one active (i.e., powered) element such as an operational amplifier (or “op-amp”).
Another common delineation among filters is between single-ended filters and multiple-ended filters. Single-ended filters have only a single input node and a single output node. Multiple-ended filters have multiple input nodes and multiple output nodes. A common type of multiple-ended filters is double-ended filters, which have two input nodes and two output nodes. Double-ended filters are often referred to as “differential” filters (having (two) “differential” input nodes and (two) “differential” output nodes). For illustration and not limitation, this disclosure discusses single-ended and differential filters rather than single-ended and multiple-ended filters.
Moreover, another common delineation among filters is according to what the filter does, i.e., according to the type of transfer function collectively realized by the properties and arrangement of the filter's composite elements. As is known to those of skill in the art, some common types of filters when categorized according to transfer function—are low-pass filters, high-pass filters, band-pass filters, band-stop (or “notch”) filters, and all-pass filters, though many other types abound.
Using a single-ended topology by way of example and not limitation, one common type of active filter includes an op-amp and a passive signal-filtering RC (resistor-capacitor) network as a feedback path between (i) the output node of the filter (which is coupled to the output node of the op-amp) and (ii) one of the two inputs of the op-amp. The passive signal-filtering RC network is typically also separately coupled to the input node of the filter. It is the collective properties and arrangement of this passive signal-filtering RC network that cause the filter as a whole to exhibit its characteristic transfer function, i.e., that cause the filter to be a low-pass filter, a high-pass filter, a band-pass filter, or perhaps another type. Such filters are generally and herein referred to as “active RC filters.”
As is also the case with filters having other topologies, and as is known to those of skill in the art, active RC filters are often characterized by a set of performance metrics (or “performance factors”), some common examples of which are the gain (Ho), the bandwidth (ωo), the quality factor (“Q factor” or just “Q”), and the damping ratio (“zeta (ζ)” or just “Z”). These performance metrics are discussed in a general way below, though this discussion is meant to aid the reader and not to restrict the discussed performance metrics to the definitions and explanations that are given below. And there are other examples of performance metrics as well.
The gain of a filter is a (usually logarithmic) ratio of the signal output of the filter to the signal input of the filter. If this ratio is greater than one, the filter is said to amplify its input signal. If this ratio is less than one, the filter is said to attenuate its input signal. In various different contexts, it may be desirable to implement a filter having a large attenuating effect, a small attenuating effect, a small amplifying effect, or a large amplifying effect, among other options.
Gain can be measured and expressed in different ways, such as in terms of voltage, current, or power. For illustration and not by way of limitation, voltage gain is the type most discussed in this disclosure. The voltage gain of a filter is a (usually logarithmic) ratio of the voltage at the output node to the voltage at the input node. Those of skill in the art are familiar with transforming between and among different domains, and are aware of parallel constructs and concepts across domains (such as voltage dividers in the voltage domain and current dividers in the current domain, and the like). As such, the discussion below being in the context of the voltage domain-input voltages, output voltages, voltage dividers, and the like—is by way of example and not limitation, as those having skill in the art will readily appreciate that the constructs and concepts disclosed herein apply with equal force to other domains.
The bandwidth of a filter is a measure of the difference between what are referred to as the upper and lower cutoff frequencies of the filter, which are the upper and lower bounds of the frequency range over which the filter performs according to its characteristic transfer function. A common definition for a cutoff frequency is the frequency above which (in the case of an upper cutoff frequency) or below which (in the case of a lower cutoff frequency) the response (i.e., the output voltage) of the filter is at least 3 decibels (dB) less than the response of the filter in its operating range (i.e., between the upper and lower cutoff frequencies). Narrow-bandwidth filters are desirable in some contexts, while large-bandwidth filters are desirable in others.
The Q of a filter is a ratio of the center frequency of the operating range of the filter to the bandwidth of the filter, and as such is also a measure of what is known as the “slope” of the filter, as higher center frequencies and narrower bandwidths tend to increase the slope (in the context of a graph of the filter response as a function of the frequency of the input signal), while lower center frequencies and wider bandwidths tend to decrease the slope. As such, filters with operating ranges centered on higher frequencies will generally have higher Qs than will filters with operating ranges centered on lower frequencies. And filters with small bandwidths will generally have higher Qs than will filters with large bandwidths. Z is an inverse expression of Q. Thus, filters with high Qs have low Zs, and vice versa.
Again using a single-ended topology by way of example and not limitation, active RC filters are typically arranged such that the above-mentioned passive signal-filtering RC network is connected as a feedback path between (i) the output node (which, again, is the output node of both the op-amp and the filter as a whole) and (ii) the inverting differential input (or “the inverting input,” often denoted “V−” or just “−”) of the op-amp; the other input is the non-inverting differential input (or “the non-inverting input,” often denoted “V+” or just “+”).
In such an arrangement, the higher the overall attenuation (i.e., impedance, resistance, and the like) of the passive signal-filtering RC network of the filter, the higher the gain of the filter will be. The opposite, however, is true of bandwidth: the higher the overall attenuation of the passive signal-filtering RC network of the filter, the lower the bandwidth of the filter will be. Designers therefore face tradeoffs of gain (and Q) for bandwidth, and vice versa.
The inventor has identified a need for an active RC filter having a gain-setting attenuator; i.e., an active RC filter for which the gain can be changed without resulting in a change in either the bandwidth or the Q of the filter. Moreover, when a given context demands (or would at least benefit from) filters with multiple different {gain, Q, bandwidth} profiles, designers often have no choice but to include multiple parallel signal-processing paths. The inventor has also identified a need for an active RC filter having a gain-setting attenuator with which the gain of the filter can be adjusted during operation without affecting either the bandwidth or the Q of the filter.
Those having skill in the relevant art will appreciate that elements in the figures are illustrated for simplicity and clarity, and have not necessarily been drawn to scale. For example, the dimensions of some of the elements in the figures may be exaggerated relative to other elements to help to improve understanding of various embodiments. Furthermore, the apparatus and method components have been represented where appropriate by conventional symbols in the figures, showing only those specific details that are pertinent to understanding the disclosed embodiments so as not to obscure the disclosure with details that will be readily apparent to those having skill in the relevant art having the benefit of this description.